Remark 5.1 It is worth noting that this result is new and cannot be obtained by the methods available before.
Indeed, the previously available machinery, which was developed for studying Besov spaces of variable smoothness, is much like the classical methods
for dealing with Besov spaces of constant smoothness. The methods known so far depend on pointwise estimates of the variable smoothness, and hence
are incapable of yielding Theorem 5.1 (see [1]} for details).

